gh-38181: sage.plot, sage.repl: Modularization fixes (imports), `…

…# needs`

    
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Also removing a use of `SR`, when testing for `Expression` is good
enough.

- Cherry-picked from #35095.

### 📝 Checklist

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- [ ] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: #38181
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe

src/sage/plot/graphics.py

@@ -2438,15 +2438,15 @@ def _matplotlib_tick_formatter(self, subplot, base=(10, 10),
         x_formatter, y_formatter = tick_formatter
         from matplotlib.ticker import FuncFormatter, FixedFormatter
         from sage.misc.latex import latex
-        from sage.symbolic.ring import SR
+        from sage.structure.element import Expression
         from .misc import _multiple_of_constant
         # ---------------------- Formatting x-ticks ----------------------
         if x_formatter is None:
             if scale[0] == 'log':
                 x_formatter = LogFormatterMathtext(base=base[0])
             else:
                 x_formatter = ScalarFormatter()
-        elif x_formatter in SR:
+        elif isinstance(x_formatter, Expression):
             x_const = x_formatter
             x_formatter = FuncFormatter(lambda n, pos:
                                         _multiple_of_constant(n, pos, x_const))
@@ -2475,7 +2475,7 @@ def _matplotlib_tick_formatter(self, subplot, base=(10, 10),
                 y_formatter = LogFormatterMathtext(base=base[1])
             else:
                 y_formatter = ScalarFormatter()
-        elif y_formatter in SR:
+        elif isinstance(y_formatter, Expression):
             y_const = y_formatter
             y_formatter = FuncFormatter(lambda n, pos:
                                         _multiple_of_constant(n, pos, y_const))
@@ -2763,10 +2763,10 @@ def matplotlib(self, filename=None,
         if stylesheet in plt.style.available:
             plt.style.use(stylesheet)
 
-        from sage.symbolic.ring import SR
+        from sage.structure.element import Expression
         # make sure both formatters typeset or both don't
         if not isinstance(tick_formatter, (list, tuple)):
-            if tick_formatter == "latex" or tick_formatter in SR:
+            if tick_formatter == "latex" or isinstance(tick_formatter, Expression):
                 tick_formatter = (tick_formatter, "latex")
             else:
                 tick_formatter = (tick_formatter, None)

src/sage/plot/hyperbolic_regular_polygon.py

@@ -17,16 +17,18 @@
 #                  https://www.gnu.org/licenses/
 #*****************************************************************************
 
+from sage.matrix.constructor import matrix
+from sage.misc.decorators import options, rename_keyword
+from sage.misc.functional import is_odd
+from sage.misc.lazy_import import lazy_import
 from sage.plot.hyperbolic_polygon import HyperbolicPolygon
-from sage.plot.all import Graphics
+from sage.plot.plot import Graphics
 from sage.rings.cc import CC
 from sage.rings.integer import Integer
-from sage.misc.decorators import options, rename_keyword
-from sage.symbolic.constants import pi, e
-from sage.functions.hyperbolic import arccosh
-from sage.functions.trig import sin, cos, cot
-from sage.misc.functional import is_odd
-from sage.matrix.constructor import matrix
+
+lazy_import("sage.functions.hyperbolic", "arccosh")
+lazy_import("sage.functions.trig", ["sin", "cos", "cot"])
+lazy_import("sage.symbolic.constants", ["pi", "e"])
 
 
 class HyperbolicRegularPolygon(HyperbolicPolygon):

src/sage/plot/plot3d/plot3d.py

@@ -147,15 +147,16 @@ def f(x,y): return math.exp(x/5)*math.cos(y)
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from .tri_plot import TrianglePlot
-from .index_face_set import IndexFaceSet
-from .shapes import arrow3d
-from .base import Graphics3dGroup
+from sage.misc.lazy_import import lazy_import
+from sage.misc.sageinspect import sage_getargspec, is_function_or_cython_function
 from sage.plot.colors import rainbow
-from .texture import Texture
+from sage.plot.plot3d.base import Graphics3dGroup
+from sage.plot.plot3d.index_face_set import IndexFaceSet
+from sage.plot.plot3d.shapes import arrow3d
+from sage.plot.plot3d.texture import Texture
+from sage.plot.plot3d.tri_plot import TrianglePlot
 
-from sage.functions.trig import cos, sin
-from sage.misc.sageinspect import sage_getargspec, is_function_or_cython_function
+lazy_import("sage.functions.trig", ["cos", "sin"])
 
 
 class _Coordinates:

src/sage/repl/display/formatter.py

@@ -7,7 +7,7 @@
 contains a new facility for displaying lists of matrices in an easier
 to read format::
 
-    sage: [identity_matrix(i) for i in range(2,5)]
+    sage: [identity_matrix(i) for i in range(2, 5)]                                     # needs sage.modules
     [
                     [1 0 0 0]
            [1 0 0]  [0 1 0 0]
@@ -236,19 +236,23 @@ def _ipython_float_precision_changed(change):
             sage: shell.run_cell('matrix.options.precision')  # indirect doctest        # needs sage.modules
             None
         """
-        from sage.matrix.constructor import options
-        s = change.new
-        if not s:
-            # unset the precision
-            options.precision = None
+        try:
+            from sage.matrix.constructor import options
+        except ImportError:
+            pass
         else:
-            try:
-                prec = int(s)
-                if prec >= 0:
-                    options.precision = prec
-                # otherwise ignore the change
-            except ValueError:
-                pass
+            s = change.new
+            if not s:
+                # unset the precision
+                options.precision = None
+            else:
+                try:
+                    prec = int(s)
+                    if prec >= 0:
+                        options.precision = prec
+                    # otherwise ignore the change
+                except ValueError:
+                    pass
 
 
 class SagePlainTextFormatter(PlainTextFormatter):

src/sage/repl/image.py

@@ -1,4 +1,5 @@
 # sage_setup: distribution = sagemath-repl
+# sage.doctest: needs pillow
 """
 Sage Wrapper for Bitmap Images
 

src/sage/repl/ipython_kernel/interact.py

@@ -34,15 +34,18 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from ipywidgets.widgets import SelectionSlider, ValueWidget, ToggleButtons
-from ipywidgets.widgets.interaction import interactive, signature
 from collections import OrderedDict
 from collections.abc import Iterable, Iterator
-from .widgets import EvalText, SageColorPicker
-from sage.structure.element import parent
+
+from ipywidgets.widgets import SelectionSlider, ValueWidget, ToggleButtons
+from ipywidgets.widgets.interaction import interactive, signature
+
 import sage.rings.abc
+
 from sage.misc.lazy_import import lazy_import
-from sage.structure.element import Matrix
+from sage.repl.ipython_kernel.widgets import EvalText, SageColorPicker
+from sage.structure.element import Matrix, parent
+
 lazy_import("sage.plot.colors", "Color")
 
 
@@ -173,6 +176,7 @@ def widget_from_single_value(cls, abbrev, *args, **kwds):
 
             return input_grid(abbrev.nrows(), abbrev.ncols(),
                               default=abbrev.list(), to_value=abbrev.parent())
+
         if isinstance(abbrev, Color):
             return SageColorPicker(value=abbrev.html_color())
         # Get widget from IPython if possible

src/sage/repl/ipython_kernel/widgets.py

@@ -101,7 +101,7 @@ class TransformWidget():
         sage: from ipywidgets import ToggleButtons
         sage: from sage.repl.ipython_kernel.widgets import TransformWidget
         sage: class TransformToggleButtons(TransformWidget, ToggleButtons): pass
-        sage: w = TransformToggleButtons(options=["pi", "e"], transform=lambda x: x+x)
+        sage: w = TransformToggleButtons(options=["pi", "e"], transform=lambda x: x + x)
         sage: w
         TransformToggleButtons(options=('pi', 'e'), value='pi')
         sage: w.get_interact_value()
@@ -240,7 +240,8 @@ class TransformIntRangeSlider(TransformWidget, IntRangeSlider):
     EXAMPLES::
 
         sage: from sage.repl.ipython_kernel.widgets import TransformIntRangeSlider
-        sage: w = TransformIntRangeSlider(min=0, max=100, value=(7,9), transform=lambda x: x[1]-x[0])
+        sage: w = TransformIntRangeSlider(min=0, max=100, value=(7, 9),
+        ....:                             transform=lambda x: x[1] - x[0])
         sage: w
         TransformIntRangeSlider(value=(7, 9))
         sage: w.get_interact_value()
@@ -257,7 +258,8 @@ class TransformFloatRangeSlider(TransformWidget, FloatRangeSlider):
     EXAMPLES::
 
         sage: from sage.repl.ipython_kernel.widgets import TransformFloatRangeSlider
-        sage: w = TransformFloatRangeSlider(min=0, max=100, value=(7,9), transform=lambda x: x[1]-x[0])
+        sage: w = TransformFloatRangeSlider(min=0, max=100, value=(7, 9),
+        ....:                               transform=lambda x: x[1] - x[0])
         sage: w
         TransformFloatRangeSlider(value=(7.0, 9.0))
         sage: w.get_interact_value()
@@ -274,7 +276,7 @@ class TransformText(TransformWidget, Text):
     EXAMPLES::
 
         sage: from sage.repl.ipython_kernel.widgets import TransformText
-        sage: w = TransformText(value="hello", transform=lambda x: x+x)
+        sage: w = TransformText(value="hello", transform=lambda x: x + x)
         sage: w
         TransformText(value='hello')
         sage: w.get_interact_value()
@@ -291,7 +293,7 @@ class TransformTextarea(TransformWidget, Textarea):
     EXAMPLES::
 
         sage: from sage.repl.ipython_kernel.widgets import TransformTextarea
-        sage: w = TransformTextarea(value="hello", transform=lambda x: x+x)
+        sage: w = TransformTextarea(value="hello", transform=lambda x: x + x)
         sage: w
         TransformTextarea(value='hello')
         sage: w.get_interact_value()
@@ -371,7 +373,10 @@ class Grid(TransformWidget, HBox, ValueWidget):
         sage: from sage.repl.ipython_kernel.widgets import Grid
         sage: w = Grid(2, 2, lambda i,j: Text(value="%s,%s"%(i,j)))
         sage: w
-        Grid(value=[['0,0', '0,1'], ['1,0', '1,1']], children=(Label(value=''), VBox(children=(Text(value='0,0'), Text(value='1,0'))), VBox(children=(Text(value='0,1'), Text(value='1,1')))))
+        Grid(value=[['0,0', '0,1'], ['1,0', '1,1']],
+             children=(Label(value=''),
+                       VBox(children=(Text(value='0,0'), Text(value='1,0'))),
+                       VBox(children=(Text(value='0,1'), Text(value='1,1')))))
         sage: w.get_interact_value()
         [['0,0', '0,1'], ['1,0', '1,1']]
     """

src/sage/repl/preparse.py

@@ -64,7 +64,7 @@
     4
     sage: 87.factor()
     3 * 29
-    sage: 15.10.sqrt()
+    sage: 15.10.sqrt()                                                                  # needs sage.rings.real_mpfr
     3.88587184554509
     sage: preparse('87.sqrt()')
     'Integer(87).sqrt()'
@@ -83,7 +83,7 @@
 Symbolic functional notation::
 
     sage: # needs sage.symbolic
-    sage: a=10; f(theta, beta) = theta + beta; b = x^2 + theta
+    sage: a = 10; f(theta, beta) = theta + beta; b = x^2 + theta
     sage: f
     (theta, beta) |--> beta + theta
     sage: a
@@ -1032,7 +1032,7 @@ def parse_ellipsis(code, preparse_step=True):
         '(ellipsis_range(1,2,Ellipsis,n))'
         sage: parse_ellipsis("for i in (f(x) .. L[10]):")
         'for i in (ellipsis_iter(f(x) ,Ellipsis, L[10])):'
-        sage: [1.0..2.0]
+        sage: [1.0..2.0]                                                                # needs sage.rings.real_mpfr
         [1.00000000000000, 2.00000000000000]
 
     TESTS:

src/sage/repl/user_globals.py

@@ -164,8 +164,9 @@ def initialize_globals(all, g=None):
 
 def get_global(name):
     """
-    Return the value of global variable ``name``. Raise ``NameError``
-    if there is no such global variable.
+    Return the value of global variable ``name``.
+
+    Raise :class:`NameError` if there is no such global variable.
 
     INPUT: